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Is There an Analog of Nesterov Acceleration for MCMC?

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arxiv 1902.00996 v2 pith:SJDVUOMS submitted 2019-02-04 stat.ML cs.LGcs.NAmath.NA

Yi-An Ma , Niladri Chatterji , Xiang Cheng , Nicolas Flammarion , Peter Bartlett , Michael I. Jordan This is my paper · ORCID
classification stat.MLcs.LGcs.NAmath.NA
keywords algorithmlangevinacceleratedfunctionalmcmcunderdampedaccelerationanalog
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We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an underdamped form of the Langevin algorithm performs accelerated gradient descent in this metric. To characterize the convergence of the algorithm, we construct a Lyapunov functional and exploit hypocoercivity of the underdamped Langevin algorithm. As an application, we show that accelerated rates can be obtained for a class of nonconvex functions with the Langevin algorithm.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithm

    stat.ML 2019-08 conditional novelty 8.0 of 10

    A third-order Langevin MCMC algorithm is proven to sample from smooth log-concave distributions in O(d^(1/4)/epsilon^(1/2)) iterations for generalized linear model potentials, improving on the earlier d^(1/3) barrier.

  2. Accelerated Information Gradient flow

    math.OC 2019-09 conditional novelty 6.0 of 10

    The authors derive and analyze accelerated Nesterov-type gradient flows in probability space under four information metrics and use them to build faster mean-field MCMC sampling algorithms.

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